Description Usage Arguments Details Value References See Also
A binary relation R is total (or strong complete), iff for all x, y we have xRy or yRx.
1 2 3 |
R |
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set. |
Note that each total relation is also reflexive,
see rel_is_reflexive
.
rel_is_total
determines if a given binary relation
R
is total.
The algorithm has O(n^2) time complexity,
where n is the number of rows in R
.
If R[i,j]
and R[j,i]
is NA
for some (i,j), then the functions outputs NA
.
The problem of finding a total closure or reduction is not well-defined in general.
When dealing with preorders, however, the following
closure may be useful, see (Gagolewski, 2013).
Fair totalization of R, performed by
rel_closure_total_fair
, is the minimal superset R' of R
such that if not xRy and not yRx
then xR'y and yR'x.
Even if R
is transitive, the resulting relation
might not necessarily fulfil this property.
If you want a total preorder,
call rel_closure_transitive
afterwards.
Missing values in R
are not allowed and result in an error.
rel_is_total
returns a single logical value.
rel_closure_reflexive
returns a logical square matrix.
dimnames
of R
are preserved.
Gagolewski M., Scientific Impact Assessment Cannot be Fair,
Journal of Informetrics 7(4), 2013, pp. 792-802.
Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7
Other binary_relations: check_comonotonicity
,
pord_nd
, pord_spread
,
pord_weakdom
, rel_graph
,
rel_is_antisymmetric
,
rel_is_asymmetric
,
rel_is_cyclic
,
rel_is_irreflexive
,
rel_is_reflexive
,
rel_is_symmetric
,
rel_is_transitive
,
rel_reduction_hasse
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